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《Journal of Pure and Applied Algebra》2022,226(8):106948
Let be a Henselian discrete valued field with residue field of characteristic , and be the Brauer p-dimension of K. This paper shows that if , for some . It proves that if and only if . 相似文献
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In this paper, the authors discuss a generalization of Lappan’s theorem to higher dimensional complex projective space and get the following result: Let f be a holomorphic mapping of ? into Pn(C), and let H1, · · · , Hq be hyperplanes in general position in Pn(C).Assume that sup {(1 ? |z|2)f?(z) : z ∈ q[ j=1 f?1(Hj )o < ∞,if q ≥ 2n2 + 3, then f is normal. 相似文献
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Laterally-coupled ridge-waveguide distributed feedback lasers fabricated without epitaxial regrowth steps have the advantages of process simplification and low cost. We present a laterally coupled grating with slots. The slots etched between the ridge and grating area are designed to suppress the lateral diffusion of carriers and to reduce the influence of the aspect-ratio-dependent-etching effect on the grating morphology in the etching process. Moreover, the grating height in this structure can be decreased to lower the aspect ratio significantly, which is advantageous over the conventional laterally coupled ridge waveguide gratings. The effects of five main structural parameters on the coupling characteristics of gratings are studied by MODE Solutions. It is found that varying the lateral width of the grating can be used as an effective way to tune the coupling strength; narrow slots (100 nm and 300 nm) and wide ridge (2 μm-4 μm) promote the stability of grating coupling coefficient and device performance. It is important to note that the grating bottom should be fabricated precisely. The comparative study of carrier distribution and mode field distribution shows that the introduction of narrow slots can strengthen the competitive advantage and stability of the fundamental mode. 相似文献
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Asymmetric mode transformation in waveguide is of great significance for on-chip integrated devices with one-way effect, while it is challenging to achieve asymmetric nonlinear-mode-conversion (NMC) due to the limitations imposed by phase-matching. In this work, we theoretically proposed a new scheme for realizing asymmetric NMC by combining frequency-doubling process and periodic PT symmetric modulation in an optical waveguide. By engineering the one-way momentum from PT symmetric modulation, we have demonstrated the unidirectional conversion from pump to second harmonic with desired guided modes. Our findings offer new opportunities for manipulating nonlinear optical fields with PT symmetry, which could further boost more exploration on on-chip nonlinear devices assisted by non-Hermitian optics. 相似文献
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Relationship between the spatial position of the seed and growth mode for single-crystal diamond grown with an enclosed-type holder 下载免费PDF全文
Wen-Liang Xie 《中国物理 B》2022,31(10):108106-108106
The relationship between the spatial position of the diamond seed and growth mode is investigated with an enclosed-type holder for single-crystal diamond growth using the microwave plasma chemical vapor deposition epitaxial method. The results demonstrate that there are three main regions by varying the spatial position of the seed. Due to the plasma concentration occurring at the seed edge, a larger depth is beneficial to transfer the plasma to the holder surface and suppress the polycrystalline diamond rim around the seed edge. However, the plasma density at the edge decreases drastically when the depth is too large, resulting in the growth of a vicinal grain plane and the reduction of surface area. By adopting an appropriate spatial location, the size of single-crystal diamond can be increased from 7 mm × 7 mm × 0.35 mm to 8.6 mm × 8.6 mm × 2.8 mm without the polycrystalline diamond rim. 相似文献
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Michele Colturato 《Mathematical Methods in the Applied Sciences》2020,43(10):6598-6626
We consider the sliding mode control (SMC) problem for a diffuse interface tumor growth model coupling a Cahn–Hilliard equation with a reaction–diffusion equation perturbed by a maximal monotone nonlinearity. We prove existence and regularity of strong solutions and, under further assumptions, a uniqueness result. Then, we show that the chosen SMC law forces the system to reach within finite time a sliding manifold that we chose in order that the tumor phase remains constant in time. 相似文献
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利用单相机所采集的图像实现了对光滑高反射表面面形的直接检测.首先利用相机获取参考平面在标准平面镜中的镜像,然后通过参考平面上的点与归一化成像平面上图像点之间的密集折返对应关系,求得待测镜面的深度距离,从而实现对高反射表面面形的测量.通过光线追迹将该测量过程转化为求解物空间中关于两对应光线束之间的相交问题.以相位为载体获取面形梯度分布,求得该表面的法向量场,并求解相应的反射光线束.通过光线追迹对该光线束与相应入射光线束求“交点”检测高反射表面.对标准平面镜进行实验检测,测量得到的面形平面度为0.19 mm.采用传统方法与本文所提方法对汽车后视镜进行检测,所得检测结果对应点之间的平均距离为0.15 mm,验证了本文方法检测镜面面形的有效性. 相似文献